Total Path Length in Power-Weight Recursive Trees: Martingale Limits and Global Fluctuations NC5Z77F6H4

URI	`m2://res/NC5Z77F6H4`
Kind	preprint
Creators	Marek Gałązka, Hanna Wdowicka
Date	2026-09-30
MSC	60-XX, 05-XX
Subjects	arxiv math.PR, arxiv math.CO
Scope	in

Expressions

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Uniform recursive tree benchmark	statement	corollary 6.5	arxiv
Bernoulli representation	statement	proposition 2.1	arxiv
4EK5YK0E00	statement	proposition 4.3	arxiv
Generation complexity	statement	corollary 3.2	arxiv
Weighted-depth martingale	statement	proposition 5.1	arxiv
80V0VY315K	statement	corollary 4.4	arxiv
Exact innovation representation	statement	theorem 5.2	arxiv
Random constant-time limit	statement	theorem 7.1	arxiv
Exact innovation variance	statement	proposition 8.1	arxiv
Exact expectation and phase transition	statement	theorem 4.1	arxiv
Two-sample parent rule	statement	proposition 3.1	arxiv
Average root-traversal complexity	statement	corollary 4.2	arxiv
Path-length limit for deterministic weights	statement	theorem 6.2	arxiv
Square summability for deterministic weights	statement	lemma 6.1	arxiv
Power-weight path-length limit	statement	corollary 6.3	arxiv
Young-age path-length variance	statement	theorem 8.2	arxiv
Local equality, global separation	statement	corollary 8.3	arxiv
X8MPZHA8P5	statement	corollary 9.1	arxiv
Innovation variance recurrence	statement	proposition 5.3	arxiv
Asymptotics of the Bernoulli parameters	statement	lemma 2.3	arxiv
Pathwise phase transition	statement	corollary 6.6	arxiv